U.S. Sens. Lamar Alexander, R-Tenn., right, Rand Paul, R-Ky., speak to reporters at a charter school in Nashville on Monday. Paul said he was "very supportive" of Alexander, but stopped short of endorsing his re-election bid.

But the Tea Party firebrand said Monday that&#8217;s not an endorsement of two-term incumbent Alexander as the two senators stood side by side in Nashville.

Paul&#8217;s comments came as he and Alexander met with reporters before heading into a joint forum they sponsored on public charter schools.

With Tennessee and national Tea Party groups and other hard-right conservatives vowing to field a GOP primary challenge to Alexander next year, Paul, a potential 2016 presidential candidate, was asked if he plans to endorse the Tennessean. &#8220;I think it&#8217;s a sort of a fun parlor game that the media gets involved with,&#8221; Paul chided reporters. &#8220;I&#8217;d rather not go there but I hate to be painted as, &#8216;Oh, I&#8217;ve come here and I&#8217;m not endorsing him,&#8217; OK, because I think that&#8217;s the wrong message to send,&#8221; Paul continued. He said he hopes Alexander &#8220;accepts that.&#8221;

&#8221;I hope he wins re-election and I&#8217;m very supportive of him, he said. &#8220;I&#8217;m here for education. I&#8217;m here to learn from Sen. Alexander&#8217;s expertise and Tennessee&#8217;s.&#8221;

On Sunday, Paul attended a Williamson County fundraiser for state Sen. Jack Johnson, R-Franklin, at which he endorsed Johnson, who has no opponent.

Alexander said he does understand and noted the only other U.S. senator who has endorsed him at this point is fellow Tennessee Republican Bob Corker, who joined most of the state GOP&#8217;s political establishment in doing so.

&#8220;We&#8217;re not here to endorse each other,&#8221; Alexander said. &#8220;What I try to do is earn the respect of my colleagues. And Rand Paul has certainly earned my respect for the way he speaks out and works on education, and I hope I can earn his.&#8221;

Alexander, the ranking Republican on the Senate Health, Education, Labor and Pensions Committee, said, &#8220;We&#8217;re not here about endorsements. We&#8217;re here about how can we help teachers, and parents and children, and I appreciate very much what he has to say.&#8221;

The senator recently began airing a spot featuring Paul and touting the two senators&#8217; role blocking the U.S. Army Corps of Engineers&#8217; plans to stop Tennesseans and Kentuckians from fishing below dams on the Cumberland River.

&#8220;Nobody wants to say no to Lamar Alexander,&#8221; Paul says in a video taken from a news conference and used in the ad.

But Paul&#8217;s aides later said that shouldn&#8217;t be construed as an endorsement, and Alexander has noted it was not intended to imply that, although Tennessee Tea Party leaders fumed.

&#8220;My TV ad, I hope, gives the impression that we&#8217;re pretty effective when it comes to defending the rights of fishermen and that if we can be half as effective at improving the schools, the kids will be a lot better off,&#8221; Alexander said.

Later, Alexander and Paul listened to state Education Commissioner Kevin Huffman as well as a former student, parents of students and officials at Kipp Academy, a grade 5-8 public charter school.

Republican Gov. Bill Haslam and Huffman have pushed publicly funded but privately operated charter schools as part of the solution to improving public education.

Alexander and Paul are working on a Republican alternative to Senate majority Democrats&#8217; education bill. The GOP alternative would promote more school choice.